On modulus of convexity of quasi-Banach spaces.

The aim of this report is to study modulus of convexity δB of a quasi-Banach space B. We prove that δB is convex, continuous, nondecreasing and for arbitrary uniformly convex quasi-Banach space B, δB(∊) = 1 - 1/C√1 - ∊2C2/4 . We also prove that a quasi-Banach space B is uniformly convex if and only if δB(∊) ≥ 0. Moreover we prove that a non-trivial quasi-Banach space B is uniformly non-square if and only if δB(∊) > 0. [ABSTRACT FROM AUTHOR]